1. Field of Invention
The present invention relates to cryptographic systems, and more particularly to a method and system for generating a pair of public key and secret key for cryptographic systems using identity-based information as public keys.
2. Description of Related Arts
Experts in Cryptography used to design and analyze a cipher by hunch and belief. Cryptography has become a field of science since 1949 when Sharmon published a theory regarding cryptographic system, so as to establish a theory foundation thereof. In 1976, the paper “New Directions in Cryptography” published by Diffie and Hellman led to a revolution in cryptography. It was the first time to demonstrate a confidential communication between the receiving end and sending end without secret keys transmission. This also opened a new era for public-key cryptography.
There are cryptographic systems, secret-key (or private-key) and pubic-key. In a secret-key cryptographic system, encryption is symmetric to decryption. It is so disadvantageous that before transmitting any encrypted document, a pre-transmitting cipher K for security transmission has to be used, which is usually infeasible.
In a public-key cryptographic system, pubic-key can be separated with secret-key, and the receiving and sending terminals can transmit encrypted document without exchanging secret-keys in advance. Diffie and Hellman suggested using the complexity in computation to design an encrypted algorithm. They pointed out the np-problem, which cannot be solved in a definite time using a known technique. A cipher is designed by trapping an object into the complexity of a one-way function. This is the basic principle to design public-key cryptographic system. The security means security in computation. However, no function is proved one-way so far.
The most famous is RSA and applied for a U.S. patent, which was sold for twenty billion dollars in 1996. Its security concern is based on the difficulty in factorizing a big integral. It requires that modulus n=pq has to be big enough. So far, 130-digit numbers have been factorized. Based on security consideration, 154-digit numbers are not enough to provide high degree of security. The possibility is 50% when using Las Vegas algorithm to factorize n, and based on the theory of same-modulus attack, the same modulus n should not be shared between different users. RSA algorithm suffers its own disadvantage of same-phase property which should be changed by random combination or one-way transformation. In addition, circular attack generates stagnant point in RSA so that p and q cannot be too close, and encrypted index b and decrypted index a cannot be too small. Furthermore, RSA needs huge amount of random prime numbers and it is possible that a non-prime number can be mistakenly regarded as a prime number. Adopting two-time screening method to factorize n=pq, 106 integrals were factorized with hundreds of work stations in 1994.
In addition, ElGamal algorithm has the property of uncertainty which is widely applied in cryptographic agreements. Its security is based on the difficulty in discrete data but it can be solved by exhaustive search. Shanks algorithm is a method in compromise of time and space. There are also Rabin algorithm, Merkle-Hellman bag pack algorithm, Chor-Rivest algorithm, McEliece Algorithm, Ellipse curve cipher algorithm, Limited automation algorithm and Public-key algorithm based on identity. The above algorithms have their own advantages and limitations.